Static corrections versus dynamic correlation effects in the valence band Compton profile spectra of Ni

We compute the Compton profile of Ni using the local density approximation of density functional theory supplemented with electronic correlations treated at different levels. The total/magnetic Compton profiles show not only quantitative but also qualitative significant differences depending on whether Hubbard corrections are treated at a mean field $+U$ or in a more sophisticated dynamic way. Our aim is to discuss the range and capability of electronic correlations to modify the kinetic energy along specific spatial directions. The second and the fourth order moments of the difference in the Compton profiles are discussed as a function of the strength of local Coulomb interaction $U$.

Figure 1

Compton profiles of Ni along the principal directions $\left[001\right],\left[110\right]$, and $\left[111\right]$. The left column compares the $\text{LSDA}+U$/DMFT results for $U=2.0$ eV. In the right column the results for $U=2.3$ eV are presented. For both calculations $J=0.9$ eV and $T=400$ K have been used. The computed profiles $\text{LSDA}+U$ (blue dashed) and $\text{LSDA}+\text{DMFT}$ (red solid) are plotted in comparison to the experimental spectra (black dotted). Data were taken from Dixon et al. [24].

Figure 2

Computed difference Compton profiles $\Delta J_{\mathbf{K}}\left(p_z\right)$ of Ni along the $\left[001\right]$ direction for the values $U=2.0$ eV (black dashed) and $U=2.3$ eV (red solid).

Figure 3

Computed difference Compton profiles $\Delta J_{\mathbf{K}}\left(p_z\right)$ of Ni along the $\left[110\right]$ direction for the values $U=2.0$ eV (black dashed) and $U=2.3$ eV (red solid).

Figure 4

Computed difference Compton profiles $\Delta J_{\mathbf{K}}\left(p_z\right)$ of Ni along the $\left[111\right]$ direction for the values $U=2.0$ eV (black dashed) and $U=2.3$ eV (red solid).

Figure 5

Theoretical Compton profile anisotropies of Ni. Panel (a) The anisotropy computed within LSDA. Panels (b) and (c) show the $\text{LSDA}+U$ and $\text{LSDA}+\text{DMFT}$ results for $U=2.3$ eV, $J=0.9$ eV, and $T=400$ K. Comparison with the experimental anisotropy is presented in panel (c).

Figure 6

Theoretical Compton profile anisotropies of Ni in comparison with the experimental measurements. LSDA/$\text{LSDA}+U$ results, panels (a)/(b) over-/underestimate the anisotropy data. DMFT results are in good agreement with the experimental spectra in the range $0<p_z<0.2$ a.u. $\text{LSDA}+U$ and $\text{LSDA}+\text{DMFT}$ parameters are $U=2.3$ eV, $J=0.9$ eV, and $T=400$ K.

Figure 7

Averaged fourth (second, in inset) order moments of the difference Compton profiles computed within DMFT (red solid) and $\text{LSDA}+U$ (black dashed), for the Coulomb parameters $U=2 \mathrm{eV}/2.3$ eV, $J=0.9$ eV, and $T=400$ K.